We start by solving the equation step by step:

\[
3x + 5 + 4x = 7\left(x + \frac{5}{7}\right)
\]

### Step 1: Simplify both sides
On the left-hand side, combine like terms:
\[
3x + 4x + 5 = 7x + 5
\]
This simplifies to:
\[
7x + 5 = 7x + 5
\]

### Step 2: Analyze the equation
Now we have:
\[
7x + 5 = 7x + 5
\]

This equation is true for all values of \( x \), meaning it's an **identity**. Therefore, the solution is:

\[
\boxed{x \in \mathbb{R}} \quad \text{(All real numbers)}
\]

Would you like more details on this solution, or do you have any questions?

### Related Questions:
1. What are the conditions for an equation to be an identity?
2. How can you recognize equations with no solutions?
3. Can equations like this ever have a specific solution?
4. What is the difference between an identity and a conditional equation?
5. How can identities be used in practical applications?

### Tip:
Always check if the equation simplifies to an identity or a contradiction early on to save time solving.

Learn how to solve the linear equation 3x + 5 + 4x = 7(x + 5/7) with a step-by-step approach. This problem covers algebraic concepts like combining like terms, distribution, and identifying identities. Suitable for students in Grades 8-10.

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